Physics Lecture 6

Unit 2

Chapter 5 : Wave motion

Dr. Mohamed Adel

Mo.adel@pt.cu.edu.eg

Wave motion

Wave motion

It’s a type of periodic motion in which medium particles vibrate An transfer energy.

So, the wave is: It's a disturbance that propagates energy in the direction of propagation.

Examples on different types of waves:

Radio waves - Water waves - Light waves

- Sound waves.

Classification of the types of waves:

Types of waves

Mechanical waves

Longtudinal waves

Transverse waves

Electromagnetic waves

Transverse waves

Mechanical waves Vs. electromagnetic waves:

Mechanical wave Electromagnetic wave

A disturbance which needs medium

to travel through.

A disturbance which doesn’t need

medium to travel through.

Has relatively low speed.(( speed

of sound))

Has great speed (( speed of light))

Transverse and longitudinal. Transverse only.

Examples:

Water waves – sound waves –

pendulum – tuning or vibrating fork

– stretched wire – Yoyo

Examples :

Light waves – radio waves – X rays –

Gamma rays

Vibrations and oscillatory motion:

Before we start the explanation of this part we should recognize on the concepts which are related

to the vibratory motion:

1- Displacement

It’s the distance of the vibrating body

away from its rest ((equilibrium

point)) at any instant.

It’s a vector quantity.

It’s measured by meter.

2- Amplitude

It’s the maximum displacement made by the

oscillating body away from its rest point.

Measured in meters.

Each complete wave or vibration consists of 4

amplitudes

3 – Frequency ((F))

Hertz = oscillation/sec.

Kilohertz = 103 hertz

Megahertz = 106 hertz

Gigahertz = 109 hertz

•It’s the no. of complete oscillation made by the vibrating

body in one second.

•Measured in hertz.

Frequency rule

Frequency = 𝑁𝑜.𝑜𝑓 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑒 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛𝑠 ( 𝑛 )

𝑇𝑖𝑚𝑒 ( 𝑡 )

4 – Periodic time ((T))

• It’s the time taken by the oscillating body to make on complete oscillation.

• Measured in seconds.

Periodic time = 𝑇𝑖𝑚𝑒 ( 𝑡 )

𝑁𝑜.𝑜𝑓 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑒 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛𝑠 ( 𝑛 )

* Frequency symbol is ʋ. * Periodic time symbol is T .

F = 1

𝑇

So, Frequency is inversely proportional with time and this relation can be represented as in the opposite figure.

Relation between the frequency and the periodic time :

Examples

5 – wave length((𝝀))

•It’s the distance between two points have the same phase

• Measured in

meter.

Longitudinal waves

It’s a disturbance at which the particles

of the medium vibrate along or on the

same direction of the line of wave

propagation.

Consisted of compressions and rarefactions.

So,

One longitudinal wave = compression + rarefaction

Examples on longitudinal waves: .

Sound waves in air

1. The compression is the area of highest density and pressure.

2. The rarefaction is the area of the lowest density and pressure.

Transverse waves :

• It’s a disturbance at which the

particles of the medium vibrate

perpendicular on the line of wave

propagation

• Consisted of crests and troughs.

Transverse waves :

Important notes :

•The crest is the highest point in the transverse wave (( positive direction ))

•The trough is lowest point in the transverse wave (( Negative direction))

•The complete wave or oscillation in the transverse wave = Crest + trough.

Longitudinal waves Vs Transverse waves

Longitudinal waves Transverse waves

Medium particles vibrate around

their rest positions.

Medium particles vibrate around

their rest positions.

Medium particles vibrate along the

line of wave propagation.

Medium particles vibrate

perpendicular on the line of wave

propagation.

Consists of compressions and

rarefactions.

Consists of crests and troughs.

Move faster in solids. Move slower in solids

Occurs at the bottom of water Bec.

of low cohesion forces of water .

Occurs at the surface of water Bec.

Of high cohesion forces of water at

the surface due to the surface

tension.

Wave length = distance between the

centers of two successive

compressions or rarefactions.

Wave length = distance between the

two successive crests or troughs.

Illustrating video

The relation between the frequency, wavelength and velocity of propagation

𝑽 = 𝝀𝒇 Law of wave propagation

AS :

V is the speed of wave 𝝀 is the wave length F is the frequency

From this law we can deduce that:

•Velocity is directly proportional with frequency and wave length.

•Wave length is inversely proportional to the frequency.

F F

1. A tuning fork produces a sound wave in air having a wavelength of 1.30 meters. At what frequency does

this tuning fork vibrate?

Here we can use the wave speed equation, where the wave travels at the speed of sound through air. and use the value for the speed of sound in air 344 m/s.

v = λf

Then, f = v / λ = 344 / 1.30 = 265 Hz

Solved Example (1)

2. What will be the wave speed for the wave traveling along the violin string playing at a frequency of 392

hertz and having a wavelength of 0.760 m?

Since we know both the frequency and the wavelength of the wave,

we can calculate the wave speed on the string.

v = λ f = 0.760 X (392) = 298 m/s

Solved Example

3. A Cincinnati radio station broadcasts on a frequency of 700 kilohertz. What is the wavelength of its transmitted radio waves?

We must be careful here because, although we listen to the sounds produced by a radio broadcast, the signals sent out by the station are really electromagnetic waves that travel at the speed of light. We must have a receiver, an amplifier, and a speaker that can convert these radio waves into sound waves before our ears can detect them. The wave velocity is then: v = c = 3.00 x 108 m/s.

The wavelength of this radio signal is found as follows.

c = λf

Then λ = c / f = 3.00 x 108 / 700 x 103

or in conventional notation: λ = 300,000,000 / 700,000

λ = 4.29 x 102 m

Solved Example

4. Waves moving on a lake are observed to have a speed of 2.0 m/s, and to have a distance of 5.0 m between wave crests.

a) Determine the frequency of the waves. b) Find the period of the wave motion.

The wave speed is 2.0 m/s and the distance between wave crests, 5.0 m, is the wavelength. We can then use the wave speed equation.

a)v = λf

Then, f = v / λ = 2.0 / 5.0 = 0.40 Hz

Remember that the period is simply the reciprocal of the frequency so:

b)T = 1 / f = 1 / 0.40 Hz = 2.5 s

Solved Example